Problem 2: For the beam given below: (a) Calculate all support reactions. (b) Draw the shear diagram. Show all important values of shear. Show the sign convention within each region. (c) Draw the moment diagram. Show all important values of moment. Show the sign conventions within each region (concavity: smiley face, sad face, etc.) (d) Sketch the deflected shape. Show supports in your sketch. For your solution, let w = 2 kips/ft and L = 20 ft. A L 22 B L W C

Page I of 2 PROBLEM 2 A steel bar is bolted to another solid steel structure as shown in Figure 2. A force 400 N, which is on the plane ABCD, is acted at E. Plane ABCD is bent vertically downward at AB by 30°. Given P= 448 mm. Show 3-D Cartesian x-, y- and z- axes at point E or F. Express the force 400 N in Cartesian vector. [Ans; F = {100v6i + 200v2j – 100vZk} N or {244.949i + 282.843j-141.421k} N] Determine the moment caused by the force 400 N about (i) point F, (ii) M-N axis, and (iii) F-B axis, if AB = CD = 75mm. Express your answer in N'm. [Ans: (i) Position vector = FE = {(448+75V3)i + 150j 175k} mm; MF {28.3i + 38.9j + 127k} Nm; (ii) MN is parallel to y-axis, MMN= 38.9 Nm; (iii) uFB = 0.9035i + 0.3781j - 0.2017k; MFB = 14.7 Nm] 2a) 2b) %3D 2c) M 100 mm 150 mm 30° B P (mm) D 150 mm 45° 400 N Figure 2

B.2. Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: σ, X (M.1, M,1,)y+ (M, I. - M.1,-) z (1,1.-1²-) where My and M₂ are bending moments applied to a cross-section, and where ly, Iz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (i) What assumptions have been made in the derivation of the above expression? (ii) Indicate by means of a sketch the directions in which positive values of the bending moments My and M₂ act on a cut plane facing in the positive x direction.

An axial member consisting of two polymer bars is supported at C as shown. Bar (1) has a cross-sectional area of 680 mm² and an elastic modulus of 29 GPa. Bar (2) has a cross-sectional area of 1580 mm² and an elastic modulus of 15.2 GPa. Determine the deflection of point A relative to support C. 70 KN 0.85 m O -1.902 mm O-2.101 mm O -2.250 mm O-1.354 mm O -2.879 mm 90 kN (1) 90 kN B (2) 1.15 m

Learning Goal: To solve for forces in statically indeteminate bars with axial loads The square bar shown (Figure 1) is 70 mm thick and 4.8 m long and is fixed supported at both ends. Aload directed leftward s appled at point C, as shown, La =3.02 m from the left end. The modulus of elasticity is E = 100 GPa if point C maves 8 = 0 175 mm to the left what is the applied force? When the number of reaction forces is greater than the number of equilitrium equations, the system is Express your answer with appropriate units to three significant figures. statically indeteminste Solving for the reactions requires some additional equations. These additional View Avallable Hint(s) equations come from considering compatibility relationships (1e, continuity of displacements and relationships berween displacements ana ioads). For an axially loaded member, the compatibility relationship for the deflections can be written by setting the total relative axial displacement between the ends of the member…

The beam system shown below has a fixed support at A, roller support at C, internal hinge at B. Find the deformations at B and the maximum deflection within the span BC. Use Moment Area Theorems to find deformations

The truss shown has a pin at A and a roller at C, and is subjected to the loading as shown. The modulus of elasticity, E is 1600 ksi. If all of the members have the same cross sectional area, using the method of virtual work, find the smallest cross sectional area so that the vertical deflection at joint B does not exceed 0.4in.

Both elements have the same section and are made of the same material. Draw the shear and moment diagrams and draw the deformed Using matrix analysis techniques Realize the structural analysis (estimate forces in the supports and displacements in the free nodes) EI = 100.000 kn-m² I 10 m² H 12 m 20 N-m 目 8 40 kN 240 kw-m 2 12 m A

Determine the force in members FG, BF, and CE of the truss shown in the figure below. Let P = 29 kN. NOTE: If your answer is a compressive force then just put a negative sign. If your answer is a tensile force then just type the answer directly. (ALSO, DON'T FORGET THE UNITS) 2P 2P 30° 600 60° 60 60° 30 B. 3P 4m 4m 4m Solve the force in member FG. Solve the force in member BF. Solve the force in member CE. Q =' 21 II

3. The beam ABCD is fixed with simple support of B and C as shown in the figure below. When point A is 15 mm and point D is bent upward by 10 mm, find the loads P, Q to make point A and D equal to point B and C support points. P is acting on point A, and Q is acting on point D. The Flexible Rigidity tee is 2.5 X 106 Nm (Use Maucalay's method) 15 mm B -2.5 m تے 5m 25m 25m 10 mm